Secure k-ish nearest neighbors classifier

Abstract

The $k$-nearest neighbors ($k$NN) classifier predicts a class of a query, $q$, by taking the majority class of its $k$ neighbors in an existing (already classified) database, $S$. In secure $k$NN, $q$ and $S$ are owned by two different parties and $q$ is classified without sharing data. In this work we present a classifier based on $k$NN, that is more efficient to implement with homomorphic encryption (HE). The efficiency of our classifier comes from a relaxation we make to consider $\kappa$ nearest neighbors for $\kappa\approx k$ with probability that increases as the statistical distance between Gaussian and the distribution of the distances from $q$ to $S$ decreases. We call our classifier $k$-ish Nearest Neighbors ($k$-ish NN). For the implementation we introduce {\em double-blinded coin-toss} where the bias and output of the toss are encrypted. We use it to approximate the average and variance of the distances from $q$ to $S$ in a scalable circuit whose depth is independent of $|S|$. We believe these to be of independent interest. We implemented our classifier in an open source library based on HElib and tested it on a breast tumor database. Our classifier has accuracy and running time comparable to current state of the art (non-HE) MPC solution that have better running time but worse communication complexity. It also has communication complexity similar to naive HE implementation that have worse running time